Final answer:
The cyclists will be next to each other 22 minutes after the second cyclist crosses the railway line.
Step-by-step explanation:
The first step is to calculate the time it takes for the second cyclist to cross the railway line. Since the second cyclist crosses the line 2 minutes after the first cyclist, we can assume that they have been cycling for the same amount of time. Therefore, the time it takes for the first cyclist to cross is also 2 minutes.
Next, we need to calculate the distance that the first cyclist covers in those 2 minutes. Since the first cyclist is traveling at a speed of 30 km/hr, we can use the formula:
Distance = Speed × Time
Distance = 30 km/hr × (2/60) hr
Distance = 1 km
Now, we can set up an equation to represent the distance between the two cyclists as a function of time. Let's assume that the time is t minutes after the second cyclist crosses the railway line:
Distance = (Speed of first cyclist × t) - (Speed of second cyclist × (t - 2))
We want to find the time when the distance is equal to zero, so we can rearrange the equation:
(Speed of first cyclist × t) - (Speed of second cyclist × (t - 2)) = 0
Simplifying the equation gives:
30t - 33(t - 2) = 0
30t - 33t + 66 = 0
-3t + 66 = 0
-3t = -66
t = 22
Therefore, the cyclists will be next to each other 22 minutes after the second cyclist crosses the railway line.